# Manifold: Rolfsen Knot 8_1 # Number of Tetrahedra: 5 # Number Field x^6 - 3*x^5 - x^4 + 8*x^3 - 2*x^2 - 5*x + 3 # Approximate Field Generator -1.15044478969579 - 0.125932904208882*I # Shape Parameters y^4 - 2*y^2 + 1 -8/21*y^5 + y^4 + 8/21*y^3 - 40/21*y^2 + 1/21*y + 22/21 5/9*y^5 - 4/3*y^4 - 14/9*y^3 + 37/9*y^2 + 14/9*y - 22/9 -y^5 + 3*y^4 - 5*y^2 + y + 1 -y^5 + 2*y^4 + 2*y^3 - 4*y^2 - y + 3 # A Gluing Matrix {{1,2,1,0,0},{1,-1,0,1,-1},{1,0,0,0,0},{0,1,0,1,0},{0,-1,0,0,0}} # B Gluing Matrix {{2,0,1,0,0},{0,1,0,0,0},{0,0,2,0,0},{0,0,0,1,0},{0,0,0,0,1}} # nu Gluing Vector {3, 1, 2, 1, 0} # f Combinatorial flattening {2, 0, 1, 1, 2} # f' Combinatorial flattening {0, 0, 0, 0, 0} # 1 Loop Invariant -3*y^5 + 15/2*y^4 + 2*y^3 - 12*y^2 + 2*y + 5/2 # 2 Loop Invariant -14749836811/101680639212*y^5 + 31075828991/101680639212*y^4 + 27605839129/101680639212*y^3 - 31068299861/50840319606*y^2 - 6416689261/50840319606*y + 23046699175/50840319606 # 3 Loop Invariant -20770002140953/1559967420017302*y^4 + 15930653985155/1559967420017302*y^3 + 45243557080761/1559967420017302*y^2 - 6914694062080/779983710008651*y - 9847637455223/779983710008651 # 4 Loop Invariant 7948992566255357166268237/594819316564701567973672590*y^5 - 64671110239598414741822033/4758554532517612543789380720*y^4 - 189776349635030255031179593/4758554532517612543789380720*y^3 + 109714477996207256047872109/4758554532517612543789380720*y^2 + 1539036467054437482049149/66091035173855729774852510*y - 12581787371898715791895507/793092422086268757298230120